How to calculate maximum surface pressure a silicon wafer can withstand?

[Katana750]

Long story short, I'm working on a senior design project this semester, (involves converting a gassified biomass to a liquid ethanol using a palladium catalyst embedded in a silicon microporous matrix). I'm currently struggling what should be a fairly basic equation, but it's been too long since I've looked at such equations. Given known dimensions of the silicon wafer, (including the fact that we're removing 75% of the volume of the silicon due to the pores). The pores are small enough (3.5nm) that I assume we can generally assume the pressure relief offered by the pores is negligible.

Anyway, the question is, what equation gives us the maximum pressure the top surface of the volume can support without collapsing? (We will need to develop a pressure above the matrix to generate a reasonable flow rate through the pores).

Thanks in advance!

 

[billy_joule]

Long story short, I'm working on a senior design project this semester, (involves converting a gassified biomass to a liquid ethanol using a palladium catalyst embedded in a silicon microporous matrix). I'm currently struggling what should be a fairly basic equation,

It is not a basic equation..
See here:
http://en.wikipedia.org/wiki/Bending_of_plates

Add that to the fact your material is full of holes which act as many cracks so stress intensity factors are important:

http://en.wikipedia.org/wiki/Stress_intensity_factor

http://en.wikipedia.org/wiki/Fracture_toughness

The pores are small enough (3.5nm) that I assume we can generally assume the pressure relief offered by the pores is negligible.

The load will depend entirely on the pressure difference from one side to the other and that depends on the flow rate.

I'd suggest talking to the relevant professor at your university. Also, do some destructive testing to get some idea of the variability of your material and whether real results align with theoretical results
http://en.wikipedia.org/wiki/Destructive_testing

 

[Chestermiller]

You need to study up a little on the subject of Poroelasticity, which handles stress analysis in porous materials with internal pressurization. Look up Terzaghi Effective Stress.

Chet